Friction between two solid bodies in sliding motion takes place on a large spectrum of length and time scales: From the nanometer/second scale in an atomic force microscope up to the extremely macroscopic scales of tectonic motion. Despite our familiarity with friction, fundamental questions about its atomistic origins remain unanswered. Phenomenological laws that describe the friction in many systems were published more than 300 years ago by Amontons: The frictional force is proportional to the applied load and independent of the apparent area of contact. The atomistic origins of this simple law is still controversial. Many explanations, which seemed to be well-established until recently, have been called into question by new experimental results. Computer simulations have also revealed flaws in previous theoretical approaches and led to new insights into the atomistic processes responsible for friction. In this paper, selected computer simulation studies of friction will be discussed. Special attention will be given to how it is possible to gain insight into tribological processes that take place on macroscopic time scales with the help of atomistic computer simulations which are typically constrained to the nanometer and nanosecond regime.